Definition: You are given a question on college mathematics. You are also given 4 answer options (associated with "A", "B", "C", "D"), out of which only one is correct. You need to answer the question by selecting the correct option. You should only answer with the choice letter, not the whole answer.
Input: If f : (0, 1) → (0, 1], then which of the following could be TRUE?
I. f is one-to-one and onto.
II. The image of f is compact.
III. f is continuous, one-to-one, and onto.
(A)I only (B)II only (C)I and II only (D)I and III only

C